Surface Tension Calculator

Surface tension arises because molecules at a liquid surface experience a net inward cohesive force — they are pulled toward the bulk liquid by their neighbors but have no liquid molecules above them to balance this pull. This creates a free energy per unit area at the surface, which is the surface tension $$\gamma$$.

Force method (Wilhelmy plate / Du Noüy ring):

$$\gamma = \frac{F}{2L}$$

A thin plate or wire of length L is pulled from the liquid surface. The factor of 2 accounts for the liquid contacting both sides of the plate. The measured force F at the moment of detachment gives the surface tension directly.

Capillary rise method (Jurin's law):

$$\gamma = \frac{\rho g r h}{2\cos\theta}$$

When a narrow tube of radius r is inserted into a wetting liquid, the liquid rises to height h due to the balance between surface tension (pulling upward along the tube walls) and gravity (pulling the liquid column downward). The contact angle $$\theta$$ accounts for the wetting behavior — for water in clean glass, $$\theta \approx 0°$$ and $$\cos\theta = 1$$.

Important properties of surface tension:

• Temperature dependence: Surface tension decreases with increasing temperature because thermal motion weakens intermolecular cohesive forces. At the critical temperature, surface tension becomes zero.
• Surfactants: Detergents and soaps dramatically reduce surface tension by inserting amphiphilic molecules at the surface, disrupting the cohesive network.
• Reference values: Water at 20°C has γ ≈ 72.8 mN/m, ethanol ≈ 22.1 mN/m, mercury ≈ 485 mN/m, and typical hydrocarbon oils ≈ 25–30 mN/m.

The calculated surface tension represents the force per unit length (or energy per unit area) at the liquid surface. Compare with known values: water (72.8 mN/m), ethanol (22.1 mN/m), acetone (25.2 mN/m), mercury (485 mN/m). Values significantly different from expected may indicate contamination, incorrect temperature, or measurement errors in the input parameters.